A116623 a(0)=1, a(2n) = a(n)+A000079(A000523(2n)), a(2n+1) = 3*a(n) + A000079(A000523(2n+1)+1).

1, 5, 7, 19, 11, 29, 23, 65, 19, 49, 37, 103, 31, 85, 73, 211, 35, 89, 65, 179, 53, 143, 119, 341, 47, 125, 101, 287, 89, 251, 227, 665, 67, 169, 121, 331, 97, 259, 211, 601, 85, 223, 175, 493, 151, 421, 373, 1087, 79, 205, 157, 439, 133, 367, 319, 925, 121

Offset

0,2

Comments

Viewed as a binary tree, this is (1); 5; 7,19; 11,29,23,65; ... Related to the parity vectors of Collatz and Terras trajectories.

Links

Table of n, a(n) for n=0..56.

Index entries for sequences related to 3x+1 (or Collatz) problem

Maple

A116623 := proc(n)
    option remember;
    if n = 0 then
        1;
    elif type(n, 'even') then
        procname(n/2)+2^A000523(n) ;
    else
        3*procname(floor(n/2))+2^(1+A000523(n)) ;
    end if;
end proc: # R. J. Mathar, Nov 28 2016

Mathematica

a[n_] := a[n] = Which[n == 0, 1, EvenQ[n], a[n/2] + 2^Floor@Log2[n], True, 3a[Floor[n/2]] + 2^(1 + Floor@Log2[n])];
Table[a[n], {n, 0, 56}] (* Jean-François Alcover, Sep 01 2023 *)

Prog

(MIT/GNU Scheme)
(define (A116623 n) (cond ((zero? n) 1) ((even? n) (+ (A116623 (/ n 2)) (expt 2 (A000523 n)))) (else (+ (* 3 (A116623 (/ (- n 1) 2))) (expt 2 (+ 1 (A000523 n)))))))

Crossrefs

Cf. a(n) = A116640(A059893(n)). a(A000225(n)) = A001047(n+1). For n>= 1 a(A000079(n)) = A062709(n+1). A116641 gives the terms in ascending order and without duplicates.

Sequence in context: A337349 A028319 A116640 * A349170 A046151 A046078

Adjacent sequences: A116620 A116621 A116622 * A116624 A116625 A116626

Keyword

nonn,tabf

Author

Antti Karttunen, Feb 20 2006. Proposed by Pierre Lamothe (plamothe(AT)aei.ca), May 21 2004.

Status

approved